9 Fisher's Exact - Review: Fishers Exact Test Contingency...

Review: Fisher’s Exact Test
Contingency tables are used to summarize data from two or more
categorical variables . The simplest contingency table is a 2 × 2
table for two binary variables. The 2 × 2 tables are widely used
in practice.
The most common hypothesis testing for contingency tables is to
test whether the categorical variables are independent or not ,
e.g., whether the row and column variables are independent in a
2 × 2 table.
H
0
: the variables are independent, H
1
: the variables are not
independent .

Review: Fisher’s Exact Test
The usual χ
2
test requires that the sample size (or counts) to be
large. If the sample size (or counts) are small, the χ
2
test may
perform poorly , i.e., a 5% significance level may have an actual
significance level higher than 5%.
Recall: Significance level = P(type I error) = P(reject H
0
| H
0
holds).
We can use computer simulation to evaluate the performance of a
test: we simulate many datasets (under H
0
) and then check how
often the test rejects